State standard

This description of the standard state is an abbreviated version of that given by the lUPAC Physical Chemistry Division.  

Absolute values of some thermodynamic quantities are unknown. Only changes in values caused by changes in parameters such as temperature and pressure can be determined. It is therefore important to define a base line for substances, to which the effect of such variations may be referred. The standard state is such a base line. The properties of these standard states are indicated by use of the symbol  

For a pure substance the concept of standard state applies to the substance in a well-defined state of aggregation at a well-defined but arbitrarily chosen standard pressure. 

Historically, the defined pressure for the standard state, i.e., the standard-state pressure, has been one standard atmosphere (101 325 Pa) and most existing data use this pressure. With the growing use of SI units, continued use of the atmosphere is inconvenient. lUPAC has recommended that the thermodynamic data should be reported for a defined standard-state pressure of 100 000 Pa. The standard-state pressure in general is symbolized as Previously in all JANAF thermochemical publications, was taken as 1 atm. In the current set of JANAF Thermochemical Tables p is taken as 100 000 Pa (1 bar). It should be understood that the present change in the standard-state pressure carries no implication for standard pressures used in other contexts, e.g., the convention that normal boiling points refer to a pressure of 101 325 Pa (1 atm). 

in all the tables appearing in this publication the standard state for a pure gaseous substance is that of the substance as an (hypothetical) ideal gas at 1 bar the standard state for a pure liquid substance is that of the pure liquid under a pressure of 1 bar the standard state for a pure solid substance is that of the pure crystalline substance under a pressure of 1 bar. 

A precise definition of the term standard state has been given by lUPAC [82LAF], The fact that only changes in thermodynamic parameters, but not their absolute values, can be determined experimentally, makes it important to have a well-defined standard state that forms a base line to which the effect of variations can be referred. The lUPAC [82LAF] definition of the standard state has been adopted in the NEA-TDB project. The standard state pressure, p° = Q. MPa (1 bar), has therefore also been adopted, cf. Section II.3.2. The application of the standard state principle to pure substances and mixtures is summarised below. It should be noted that the standard state is always linked to a reference temperature, cf. Section II.3.3. 

It should be emphasised that the use of superscript, , e.g., in Af//°, implies that the compound in question is in the standard state and that the elements are in their reference states. The reference states of the elements at the reference temperature cf. Section II.3.3) are listed in Table II-6. 

We are already used to the concept of standard state in respect of pure solids, liquids and gases. The standard state of a liquid or solid substance, whether pure or in a mixture, or for a solvent is taken as the state of the pure substance at 298 K and 1 bar pressure (1 bar = 1.00 x 10 Pa) the standard state of a gas is that of the pure gas at 298 K, 1 bar pressure and exhibiting ideal gas behaviour. 

For a solute in a solution, the definition of its standard state is referred to a situation of infinite dilution it is the state (a hypothetical one) at standard molality (m°), 1 bar pressure, and exhibiting infinitely diluted solution behaviour. In the standard state, interactions between solute molecules or ions are negligible. 

When the concentration of a solute is greater than about O.lmoldm , interactions between the solute molecules or ions are significant, and the effective and real concentrations are no longer equal. It becomes necessary to define a new quantity called the activity, which is a measure of concentration but takes into account the interactions between the 

The activity of any pure substance in its standard state is defined to be unity. 

The relative activity of a solute is related to its molality by equation 6.7 where 7 is the activity coefficient of the solute, and mi and m° are the molality and standard state molality, respectively. Since the latter is defined as being unity, equation 6.7 reduces to equation 6.8. 

The additive constant term fij in Equation 2.4 is the chemical potential of species j for a specific reference state. From the preceding definitions of the various quantities involved, this reference state is attained when the following conditions hold The activity of species j is 1 (RT In cij = 0) the hydrostatic pressure equals atmospheric pressure (VjP = 0) the species is uncharged or the electrical potential is zero (ZjFE = 0) we are at the zero level for the gravitational term (rrijgh = 0) and the temperature equals the temperature of the system under consideration. Under these conditions, fij equals fij (Eq. 2.4). 

As already indicated, an activity of 1 is defined in different ways for the solute and the solvent. To describe liquid properties, such as the dielectric constant, the heat of vaporization, and the boiling point, the most convenient standard state is that of the pure solvent. For a solvent, aSoivent equals ysoiventAgoivent so the activity is 1 when the mole fraction Nso v nt is 1 (ysoivent = 1 for pure solvent). Specifically, the properties of a solvent are fully expressed when no solute is present. Thus the standard reference state for water is pure water at atmospheric pressure and at the temperature and gravitational level of the system under consideration. 

Water has an activity of 1 when Nw (see Eq. 2.8) is 1. The concentration of water on a molality basis (number of moles of a substance per kilogram of water for aqueous solutions) is then 1/(0.018016 kg mol-1) or 55.5 molal (m). The accepted convention for a solute, on the other hand, is that aj is 1 when yfj equals 1 m. For example, if yj equals 1, a solution with a 1 -m concentration of solute j has an activity of 1 m for that solute. Thus the standard state for an ideal solute is when its concentration is 1 m, in which case RT In a - is zero.2 A special convention is used for the standard state of a gas such as CO2 or O2 in an aqueous solution—namely, the activity is 1 when the solution is in equilibrium with a gas phase containing that gas at a pressure of 1 atm. (At other pressures, the activity is proportional to the partial pressure of that gas in the gas phase.) 

Conditions appropriate to the three conventions introduced for the standard state (solvent, solute, and gases) usually do not occur under biological situations. A solute is essentially never at a concentration of 1 m, neither is an important gas at a pressure of 1 atm, nor is a pure solvent present (except sometimes for water). Hence, care must be exercised when 

Because molality involves the moles of a substance per kilogram of solvent, both SI quanti ties, it is a legitimate SI unit, whereas moles per liter (m) is not recommended (the analogous SI concentration unit is moles m-3 = moles per 1000 liters = him). 

In this text, no attempt will be made to use nomenclature to distinguish between extensive and intensive properties or between an extensive property and its mass or mole-normalized specific counterpart. You should be aware, then, that quantities appearing in certain equations may represent an extensive property or its specific (e.g., per-mole) counterpart depending on the situation. For example, AG could have units of kilojoules or kilojoules per mole depending on the context. In general, this should not cause confusion, as the context and units involved will almost always be spelled out explicitly. 

Extensive thermodynamic quantities such as A//, A5, and AG are almost always normalized per mole of substance involved to produce intensive, molar-based values for these quantities. This is because it is often useful to quantify energy changes due to a reaction on a per-mole basis. Thus, when you encounter these quantities in this textbook, they almost always refer to the specific (per-mole) value. 

Calculating Extensive versus Specific Thermodynamic Quantities 

Of course the specific (per-mole) Gibbs free energy of this reaction is still AGjxn = -237 kJ/mol H2. In both cases, a quick inspection of the units makes it clear whether the AG involved is an extensive or specific (molar) quantity. 

Because most thermodynamic quantities depend on temperature and pressure, it is convenient to reference everything to a standard set of conditions. There are two types of standard conditions  

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When the same standard-state fugacity is used in both phases. Equation (5) can be rewritten... 

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

Henry s constant is the standard-state fugacity for any component i whose activity coefficient is normalised by Equation (14). ... 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

The use of Henry s constant for a standard-state fugacity means that the standard-state fugacity for a noncondensable component depends not only on the temperature but also on the nature of the solvent. It is this feature of the unsymmetric convention which is its greatest disadvantage. As a result of this disadvantage special care must be exercised in the use of the unsymmetric convention for multicomponent solutions, as discussed in Chapter 4. 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

The pressure at which standard-state fugacities are most conveniently evaluated is suggested by considerations based on the Gibbs-Duhem equation which says that at constant temperature and pressure... 

We find that the standard-state fugacity fV is the fugacity of pure liquid i at the temperature of the solution and at the reference pressure P. ... 

Standard-State Fugacity for a Noncondensable Component For a noncondensable component we write... 

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

Correlations for standard-state fugacities at 2ero pressure, for the temperature range 200° to 600°K, were generated for pure fluids using the best available vapor-pressure data. 

Below the temperature of the lowest experimental datum, standard-state fugacities were obtained by simple extrapolation. Uncertainties assigned to these fugacities are largest when the fugacities are smallest, for two reasons (1) the extrapolation... 

At temperatures above those corresponding to the highest experimental pressures, data were generated using the Lyckman correlation all of these were assigned an uncertainty of 5% of the standard-state fugacity at zero pressure. Frequently, this uncertainty amounts to one half or more atmosphere for the lowest point, and to 1 to 5 atmospheres for the highest point. 

Appendix C-2 gives constants for the zero-pressure, pure-liquid, standard-state fugacity equation for condensable components and constants for the hypothetical liquid standard-state fugacity equation for noncondensable components... 

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

Standard-state fugacities at zero pressure are evaluated using the Equation (A-2) for both condensable and noncondensable components. The Rackett Equation (B-2) is evaluated to determine the liquid molar volumes as a function of temperature. Standard-state fugacities at system temperature and pressure are given by the product of the standard-state fugacity at zero pressure and the Poynting correction shown in Equation (4-1). Double precision is advisable. 

Output FIP(I) vector (length 20) of standard-state fugacity (bars) (I = 1,N)... 

FO(I) Vector (length 20) of pure-component liquid standard-state fugacities at zero pressure or hypothetical liquid standard-... 

Thermodynamic quantities which refer to the standard state are denoted by superscript zeros ( ), e.g. AG/, AH/, AS/, the subscript denoting the temperature T of the system. 

The standard states of Ag and of Ag (aq) have the conventional definitions, but there is an ambiguity in the definition of the standard state of e. Suppose that a reference electrode R is positioned above a solution of AgN03, which in turn is in contact with an Ag electrode. The Ag electrode and R are connected by a wire. Per Faraday, the processes are... 

The adsorbed state often seems to resemble liquid adsorbate, as in the approach of the heat of adsorption to the heat of condensation in the multilayer region. For this reason, a common choice for the standard state of free adsorbate is the pure liquid. We now have... 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

The standard entropy of adsorption AS2 of benzene on a certain surface was found to be -25.2 EU at 323.1 K the standard states being the vapor at 1 atm and the film at an area of 22.5 x T per molecule. Discuss, with appropriate calculations, what the state of the adsorbed film might be, particularly as to whether it is mobile or localized. Take the molecular area of benzene to be 22 A. ... 

It is convenient to define a relative activity a. in tenns of the standard states of the reactants and products at the same temperature and pressure, where Aj = fi, =... 

Were the FlCl in its standard state, AC would equal where is the standard emf for the reaction. In general, for any reversible chemical cell without transference, i.e. one with a single electrolyte solution, not one with any kind of junction between two solutions. 

A2.1.6.7 STANDARD STATES AND STANDARD FREE ENERGIES OF FORMATION... 

Conventions about standard states (the reference states introduced earlier) are necessary because otherwise the meaning of the standard free energy of a reaction would be ambigrious. We sunnnarize the principal ones ... 

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